The book is paywalled, and not cheap. There are ways around that for those that know how, but I will not spell it out here for the sake of the forum owners. On the other hand, I have a copy, if anyone wants one;
Which you'll find is basically what I have posted upthread.5.4 A mixture of fluids
The simple fluid picture considered above has a major drawback. Since the medium (1) is made of electrons and protons (plus heavier ions in lesser concentration), and (2) is weakly collisional, it should not be pictured as a single fluid but as (at least) two fluids. This question was first addressed long ago [16], and early reviews may be found in [3] and [25].
To make things simple, we neglect the ions heavier than protons because their concentration is too small for them to affect the overall dynamics much. We therefore consider a plasma made of electrons and protons pictured as two different fluids, rather than a single fluid made of ‘average’ particles. How does this change the physics? Or rather does this bring about qualitatively new results?
Electrons and protons have opposite charges, but their masses differ by the factor mp/me ~ 1837, so that electrons have a thermal speed greater than protons by a factor of order of magnitude (mp/me)^1/2 ~ 43 (because their temperatures have generally the same order of magnitude). This has several consequences:
• whereas protons are strongly bound close to the Sun, electrons barely feel gravity; indeed, at a temperature of 10^6 K, their thermal speed ~ 5.5 × 10^6 m s−1 is nearly 10 times greater than the escape speed;
• the greater thermal speed of electrons is expected to make them carry heat much faster than do protons;
• collisions between electrons and protons exchange energy at a rate ∼ (mp/me) slower than the rate of momentum exchange, which is itself slow since the medium is weakly collisional; hence electrons and protons may have different temperatures;
• since electrons and protons are subjected to very different forces (and may have different temperatures), an electric field sets up to preserve electric quasi-neutrality
Since electrons and protons have opposite charges, electric quasi-neutrality requires them to have roughly the same number density n. Furthermore, since the radial electric current must vanish otherwise electric charge would accumulate indefinitely on the Sun, electrons and protons should have also the same radial bulk speed. The simplest generalisation of the one-fluid picture is therefore to consider two fluids having the same bulk velocity but different particle masses, temperatures and heat fluxes.
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So, if anyone thinks you can ignore G in plasma physics, then I am afraid that you are not talking about plasma physics.5.4.1 Simple balance equations
We have seen in Section 4.6 that in a static isothermal atmosphere with equal proton and electron pressures, the gravitational attraction – acting essentially on protons – tends to displace them inwards with respect to electrons. The corresponding space charge induces a radial electric field E directed outwards, which adjusts itself so that the total attraction on a proton mp Msun G/r^2 − eE is equal to the attraction on an electron eE, whence E = mp Msun G/2er^2. We shall see later that when the plasma is moving and the proton and electron pressures are not equal, the electric field has a somewhat different value.